Branching rules for Specht modules

JOURNAL OF ALGEBRA

卷:307

Article

Ellers, Harald ; Murray, John

关键词: symmetric group;    Specht module;    Jucys-Murphy element;   

DOI  :  10.1016/j.jalgebra.2006.07.032

来源: Elsevier

【 摘 要 】

Let S-lambda be a Specht module for the symmetric group Sigma(n) defined over a field of characteristic different from 2, and let L-n-1 be the sum of all transpositions in Sigma(n)-1 that do not fix n - 1. It is shown that the minimal polynomial of L-n-1 acting on S lambda has maximum possible degree. As a consequence, the indecomposable components of the restriction of S-lambda to Sigma(n)-1 coincide with the block components. Analogous results are proved for L-n+1 and the Sigma(n)+1 -module that is induced from S-lambda. (C) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

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